CRM 3.2 - Synthetic and Long Division Review

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What is synthetic division?

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Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c). It is faster than long division and is used primarily when the divisor is a linear polynomial.

Tags

CCSS.HSA.APR.D.6

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What is long division in polynomials?

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Long division in polynomials is a method used to divide a polynomial by another polynomial, similar to numerical long division. It involves dividing the leading terms, multiplying, and subtracting until the remainder is less than the degree of the divisor.

Tags

CCSS.HSA.APR.D.6

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How do you perform synthetic division?

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1. Write down the coefficients of the polynomial. 2. Use the root of the divisor (c from x - c) to set up synthetic division. 3. Bring down the leading coefficient. 4. Multiply and add down the column until finished.

Tags

CCSS.HSA.APR.D.6

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What is the remainder theorem?

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The remainder theorem states that when a polynomial f(x) is divided by (x - c), the remainder of that division is f(c).

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CCSS.HSA.APR.B.2

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What is the factor theorem?

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The factor theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

Tags

CCSS.HSA.APR.B.2

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What is the leading coefficient of a polynomial?

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The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

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What does it mean to have a zero placeholder in synthetic division?

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A zero placeholder is used in synthetic division to represent missing terms in a polynomial. For example, in the polynomial 2x^4 + 0x^3 - 3x + 5, a zero placeholder is used for the x^3 term.

Tags

CCSS.HSA.APR.D.6

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial expression.

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How do you find the b value in polynomial division?

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The b value in polynomial division refers to the coefficient of the x term in the quotient after performing the division.

Tags

CCSS.HSA.APR.D.6

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What is the significance of the divisor in polynomial division?

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The divisor is the polynomial by which another polynomial is divided. It determines the structure of the quotient and the remainder.

Tags

CCSS.HSA.APR.D.6